2 Answers
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The words follow through are not a phrasal verb in this sentence. Really, those two words should be hyphenated and then they form the single noun follow-through, which means "the act or an instance of following through (with something)."

This is also a situation where the inclusion of a serial comma between "through" and "or" might have made it more clear that the final phrase starting with "of" contains a list of three items:

poor planning

(poor) follow-through

(poor) persistence

Note that the adjective poor is meant to be applied to all three nouns (planning, follow-through, and persistence), which is not entirely clear from the sentence as written. Personally, I would have chosen to write something like this:

[...] An undisciplined person is removed from any aspect of health simply because of poor planning, inadequate follow-through, or lack of persistence.

This means the same as the original sentence, but the serial comma makes it clear that there are three items in the list, and there's an explicit negative qualifier before each of the nouns.

So, "follow through" is usually a verb. "You didn't follow through on that promise" means someone didn't actually do what they had promised to do. "You need to make sure you follow through on your golf swing" means to keeping swinging properly after hitting the ball. Two slightly different meanings originating in the same concept.

However, "follow through" can also be a noun. In a sport where you strike a ball and should follow through, the manner in which you move the tool or body part after striking the ball is referred to as "your follow through", sometimes hyphenated as follow-through.

Thus, "poor follow through" means not properly completing an action or sticking to a plan.